√x is non periodic function and cos (something) is a periodic function so here in cos‌√x→ inside periodic function there is non periodic function which always produce non periodic function. cos2x is a periodic function with period π Note: (1) When n is odd then the period of sinnθ,cosnθ,cscnθ,secnθ=2π (2) When n is even then the period of sinnθ,cosnθ,cscnθ,secnθ=π (3) When n is even/odd then the period of tannθ,cotnθ=π (3) When n is even/odd then the period of |sinnθ|,|cosnθ|,|cscnθ|,|secnθ|,|tannθ|,|cotnθ|=π cos‌√x+cos2x= non periodic function + periodic function = non periodic function